111.34.G.2: The student analyzes geometric relationships in order to make and verify conjectures.

111.34.G.2.A: use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships; and

Segment and Angle Bisectors

111.34.G.2.B: make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

Dilations

111.34.G.3: The student applies logical reasoning to justify and prove mathematical statements.

111.34.G.3.A: determine the validity of a conditional statement, its converse, inverse, and contrapositive;

Biconditional Statements
Conditional Statements

111.34.G.3.C: use logical reasoning to prove statements are true and find counter examples to disprove statements that are false;

Biconditional Statements
Conditional Statements

111.34.G.3.E: use deductive reasoning to prove a statement.

Conditional Statements

111.34.G.5: The student uses a variety of representations to describe geometric relationships and solve problems.

111.34.G.5.C: use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations; and

Circles
Rotations, Reflections, and Translations
Translations

111.34.G.6: The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems.

111.34.G.6.B: use nets to represent and construct three-dimensional geometric figures; and

Surface and Lateral Areas of Prisms and Cylinders

111.34.G.6.C: use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

3D and Orthographic Views

111.34.G.7: The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly.

111.34.G.7.A: use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

Linear Functions
Points in the Coordinate Plane
Points, Lines, and Equations

111.34.G.7.C: derive and use formulas involving length, slope, and midpoint.

Circles
Distance Formula
Slope

111.34.G.8: The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

111.34.G.8.A: find areas of regular polygons, circles, and composite figures;

Area of Triangles
Circumference and Area of Circles

111.34.G.8.C: derive, extend, and use the Pythagorean Theorem;

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

111.34.G.8.D: find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations;

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

111.34.G.8.F: use conversions between measurement systems to solve problems in real-world situations.

Unit Conversions

111.34.G.9: The student analyzes properties and describes relationships in geometric figures.

111.34.G.9.A: formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines

111.34.G.10: The student applies the concept of congruence to justify properties of figures and solve problems.

111.34.G.10.A: use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane; and

Dilations

111.34.G.10.B: justify and apply triangle congruence relationships.

Congruence in Right Triangles
Proving Triangles Congruent

111.34.G.11: The student applies the concepts of similarity to justify properties of figures and solve problems.

111.34.G.11.A: use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

Dilations

111.34.G.11.B: use ratios to solve problems involving similar figures;

Beam to Moon (Ratios and Proportions)
Perimeters and Areas of Similar Figures
Similar Figures

111.34.G.11.C: develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods; and

Perimeters and Areas of Similar Figures
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similar Figures
Similarity in Right Triangles
Sine, Cosine, and Tangent Ratios

111.34.G.11.D: describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

Perimeter and Area of Rectangles